Exercise 32 in Section 4.3 demonstrates that every polynomial is (plus or minus) the characteristic polynomial of its own companion matrix. Therefore, the roots of a polynomial p are the eigenvalues of C (p). Hence, we can use the methods of this section to approximate the roots of any polynomial when exact results are not readily available. In Exercises 1 -4, apply the shifted inverse power method to the companion matrix C ( p) of p to approximate the root of p closest to a to three decimal places.
1. p(x) = x2 + 2x - 2, α = 0
2. p(x) = x2 - x - 3, α = 2
3. p(x) = x3 - 2x2 + 1 , α = 0
4. p(x) = x3 - 5x2 + x + l, α = 5